Chemical Engineering World

Given a description of a process, the values of several process variables, and a list of quantities to be determined :

1. Choose a basis of calculation an amount or flow rate of one of the process streams.
2. Draw a flowchart and fill in all known variable values, including the basis of calculation. Then label unknown stream variables on the chart.
3. Express what the problem statement asks you to determine in terms of the labeled variables.
4. If you are given mixed mass and mole units for a stream, convert all quantities to one basis or the other.
5. Do the degree - of - freedom analysis. Count the unknowns and identify equations that relate them. The equations may be any of the these six types : "material balances", "energy balances", "process specifications", "physical property relationships and laws", "physical constraints", and "stoichiometric relations". If you count more unknown variables than equations, figure out what's wrong (the flowchart is not completely labeled, or an additional relation exists that was not counted, or one or more of your equations are not independent of the others, or the problem is underspecified or overspecified). If the number of unknowns does not equal the number of equations, there is no point wasting time trying to solve the problem.
6. If the number of unknowns equals the number of equations relating them, write the equations in an efficient order and circle the variables for which will solve.
7. Solve the equations.
8. Calculate the quantities requested in the problem statement if they have not already been calculated.
9. If a stream quantity or flow rate "ng" was given in the problem statement and another value "nc" was either choses as a basis or calculated for this stream, scale the balanced process by the ratio "ng/nc" to obtain the final result.

A liquid mixture containing 45% benzene (B) and 55% toluene (T) by mass is fed to a distillation column. A product stream leaving the top of the column (the overhead product) contains 95% mole B, and a bottom product steam contains 8% of the benzene fed to the column (meaning that 92% of the benzene leaves with the overhead product). The volumetric flow rate of the feed stream is 2000 L/h and the specific gravity of the feed mixture is 0.872. Determine the mass flow rate of the overhead product stream and the mass flow rate and composition (mass fractions) of the bottom product stream.

Step :

3. Write expressions for the quantities requested in the problem statement. In terms of the quantities labeled on the flowchart, the quantities to be determined are "m2" (the overhead product mass flow rate), "m3 = mB3 + mT3" (the bottom product mass flow rate), "xB = mB3/m3" (the benzene mass fraction in the bottom product), and "xT = 1- xB" (the toluene mass fraction). Once we determine "m2", "mB3", and "mT3", the problem is essentially solved.

4. Convert mixed units in overhead product stream.

5. Perform degree - of - freedom analysis

The problem is therefore solvable

6. Write system equations and outline a solution procedure. The variables for which equations will be solved are circled.

 

7. Do the Algebra. The four equations may be solved manually or with equation - solving software. The results are "m1 = 1744 kg/h", "mB3 = 62.8 kg/h", "m2 = 766 kg/h", and "mT3 = 915 kg/h". A total mass balance (which is the sum of the benzene and toluene balances) may be written as a check of this solution :

8. Calculate additional quantities requested in the problem statement